Cambridge Papers

by W. W. Rouse Ball

The third book contains the practical application of the propositions in the two earlier books to the solar system. I need not describe this in detail. In order to justify this application, Newton commenced [237] ]by laying down four rules which have since been accepted as binding in scientific investigations. These, as given in the third edition, are to the following effect: (1) We are not to assume more causes than are sufficient and necessary for the explanation of observed facts. (2) Hence, as far as possible, similar effects must be assigned to the same cause; for instance, the fall of stones in Europe and America. (3) Properties common to all bodies within reach of our experiments are to be assumed as pertaining to all bodies; for instance, extension. (4) Propositions in science obtained by a wide induction are to be regarded as exactly or approximately true, until phenomena or experiments show that they may be corrected or are liable to exceptions. The substance of these rules is now accepted as the basis of scientific investigation. Their formal enunciation here serves as a landmark in the history of thought.

As soon as the Copernican view of the solar system was accepted, it was natural for men to seek to explain the reason why the planets moved as they did. Descartes, in 1644, had suggested that the explanation might be found in the existence of vortices in space. This conjecture, although based on arbitrary assumptions, and in fact untenable, played an important part in the history of the subject, for it accustomed men to think that planetary phenomena might be explicable by the same laws [238] ]as are found to be true on the earth. That this was so was established by Newton in his Principia, where all the motions of the solar system were made to depend on one assumption as to the law of attraction. The question whether this law could itself be deduced from some more fundamental assumption was raised by Newton, but he could not devise a satisfactory hypothesis. It has been discussed again and again since his time, and the problem is still unsolved.

Newton’s conclusions were immediately accepted in Britain, and very rapidly by the leading mathematicians in Europe: indeed Huygens came expressly from Holland in order to make the personal acquaintance of a writer whose work promised to revolutionize the history of science. The refutation of the Cartesian hypothesis ran, however, counter to the sentiments and wishes of a certain number of philosophers, and some few years elapsed before the truth of the gravitation theory was universally admitted, but it would be ungracious to dwell further on this. In Britain the work exercised a profound influence in philosophy as well as in science, and educated men of all schools of thought acquainted themselves with the general line of Newton’s reasoning and his deductions.

That men of science and philosophers should have approved Newton’s theory is not surprising, but it is somewhat curious that it excited so little [239] ]opposition among theologians. Galileo’s discoveries of hills, vales, and (supposed) seas on the moon and planets had already suggested that life might exist there, and in the popular (but illogical) view this involved the idea of the existence of beings with spiritual and intellectual faculties not unlike those of men. Newton’s results seemed to show that there was nothing in the nature of things to differentiate the earth from the other planets, and therefore considerably strengthened the view that life might be found on them. It might well be asked whether such life, and indeed whether the mechanism of the solar system as expounded by Newton, was in accordance with Scripture. That these difficulties were not pressed against Newton’s conclusions is, I think, attributable to the fact that his theory was explicitly concerned only with non-organic matter. His own opinion was that the extension of the reign of law was an additional argument in favour of a divine creation: this view, set out at the end of the Principia and in his five letters to Bentley in 1692–93, was generally accepted by the leaders of religious thought in Britain.

Lagrange more than once remarked that Newton was not only the greatest mathematician of former days, but the most fortunate, since, as there is but one universe, it can happen to but one man in the [240] ]world’s history to be the interpreter of its laws. It is true that Newton applied his theory only to the solar system for which alone he had the necessary data, but after the publication of the Principia, no one doubted that gravity extended to the most distant regions of space. The work of Sir William Herschel and that of all later astronomers on binary and other systems rests on this hypothesis.

The influence of the Principia on dynamical astronomy has been permanent. It is not too much to say that when it was published, the theory, as there set out, had outstripped observation, but during the succeeding century large numbers of new facts were collected, and applications of the theory to new problems were made, notably by Clairaut, Euler, and Lagrange. All these researches tended to confirm it.

The demonstrations in the Principia are expressed in the language of classical geometry, and, though unnecessarily concise and difficult, their correctness is unimpeachable. That Newton could carry his calculations so far with the limited mathematics then at his command is not the least wonderful part of the performance, but it is the prerogative of genius to get great results with but scanty equipment.

Newton’s methods, which even in the seventeenth century were archaic, became in time quite out of [241] ]date. This reason, the growth of the subject, and the development of analysis made it desirable to expound dynamical astronomy afresh. Towards the end of the eighteenth century the task was undertaken by Laplace in his Mécanique Céleste. This is far more than the translation of the Principia into the language of modern analysis, for it greatly extends the theory of some branches of the subject which had been left incomplete by Newton, either on account of his not having the requisite analysis at his command or because the necessary facts were not available. Laplace acknowledged his debt to Newton, and expressed his deliberate opinion that the Principia was pre-eminent over every previous production of human genius—“so near the gods, man cannot nearer go.” A century later a fresh exposition of the subject embodying the discoveries of the nineteenth century was given by F. F. Tisserand in his Mécanique Céleste; this presents the subject in its modern form.

Newton had applied his theory to the solar system as it existed, and had not investigated its origin. We owe to Laplace the enunciation of a hypothesis as to its evolution. According to this conjecture, the solar system originated in a quantity of incandescent gas rotating round an axis through its centre of mass. Laplace assumed that as this gas cooled, it would contract, and that successive rings [242] ]would break off from its outer edge; these rings in their turn would cool, and finally condense into the planets with their satellites; while the sun represents the central core which would be left. Recent investigations show that this cannot be taken as correct without numerous modifications. Moreover every extension of our knowledge requires the introduction of alterations in the hypothesis, and this clearly suggests that the conjecture is untenable. It played, however, a useful part in its day, as suggesting a common origin for all members of the system. Perhaps I ought to add that a nebular origin had been previously outlined by Kant, who had also suggested meteoric aggregations and tidal friction as agents concerned, but these were little more than vague conjectures.

The Principia convinced its readers that the laws of mechanics, discovered by experiment on the earth, were operative throughout the solar system. It was reserved for the nineteenth century to extend the reign of law to other celestial phenomena. Newton and his successors had proved that the law of gravity extends through all parts of space where observations are possible. That the sun, stars, and planets are constituted of similar materials was generally believed; and this has now been confirmed by the use of the spectroscope which has enabled us to calculate the temperature of gaseous stars, and [243] ]specify the chemical elements comprised in them. Thus the composition of far-distant suns has been reduced to problems to be settled in our laboratories. The scientific world, however, in admitting the validity of the theory of universal gravity had implicitly accepted the principle that the reign of law, as investigated on the earth, extends throughout the universe. Thus the daring which permits us, living on a medium-sized planet attached to one of the smaller suns, to analyse the universe is, I venture to say, the direct outcome of the genius of Newton as displayed in his Principia.